A Continuous d-step conjecture for polytopes

Discrete and Computational Geometry

Volumn 41, Issue 2, 2009, Pages 318-327

  Deza, Antoine ^a   Terlaky, Tamás ^a   Zinchenko, Yuriy ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

Central path; Curvature; D Step conjecture; Diameter; Hirsch conjecture; Polytopes

Indexed keywords

EID: 65049087897     PISSN: 01795376     EISSN: 14320444     Source Type: Journal    
DOI: 10.1007/s00454-008-9096-4     Document Type: Article

References (14)

1. Dantzig, G.: Linear Programming and Extensions. Princeton University Press, Princeton (1963)
2. J.-P. Dedieu G. Malajovich M. Shub 2005 On the curvature of the central path of linear programming theory Found. Comput. Math. 5 145 171
3. Deza, A., Terlaky, T., Zinchenko, Y.: Central path curvature and iteration-complexity for redundant Klee-Minty cubes. In: Gao D. and Sherali H. (eds.) Advances in Mechanics and Mathematics, vol. III, pp. 215-248 (2007)
4. A. Deza T. Terlaky Y. Zinchenko 2008 Polytopes and arrangements: diameter and curvature Oper. Res. Lett. 36-2 215 222
5. K. Fritzsche F. Holt 1999 More polytopes meeting the conjectured Hirsch bound Discrete Math. 205 77 84
6. F. Holt V. Klee 1998 Many polytopes meeting the conjectured Hirsch bound Discrete Comput. Geom. 20 1 17
7. Grünbaum, B.: Convex Polytopes. In: Kaibel, V., Klee, V., Ziegler, G. (eds.) Graduate Texts in Mathematics. vol. 221. Springer, Berlin (2003)
8. G. Kalai D. Kleitman 1992 A quasi-polynomial bound for the diameter of graphs of polyhedra Bull. Am. Math. Soc. 26 315 316
9. V. Klee D. Walkup 1967 The d-step conjecture for polyhedra of dimension d<6 Acta Math. 133 53 78
10. Renegar, J.: A Mathematical View of Interior-Point Methods in Convex Optimization. SIAM, Philadelphia (2001)
11. Roos, C., Terlaky, T., Vial, J.-Ph.: Interior Point Methods for Linear Optimization. Springer, Berlin (2006)
12. G. Sonnevend J. Stoer G. Zhao 1991 On the complexity of following the central path of linear programs by linear extrapolation II Math. Program. 52 1-3 527 553
13. Spivak, M.: Comprehensive Introduction to Differential Geometry. Publish or Perish, Houston (1990)
14. Ziegler, G.: Lectures on Polytopes, Graduate Texts in Mathematics, vol. 152. Springer, Berlin (1995)